On the prescribed mean curvature problem on the standard $n$-dimensional ball
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In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of $\R^n$, $n\geq 3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function $H(x)$ is $\beta\in ]1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.
Abstract
In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of $\R^n$, $n\geq 3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function $H(x)$ is $\beta\in ]1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.
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